Parallel alternating Newton-like algorithm for APM
Algorithms AIMech:ParallelAlternatingNewtonAPM DRAFT
A block-alternating Newton-like method for fitting an admixture of Poisson Markov random fields through a sparsity-penalized nodewise Poisson regression surrogate, alternating topic coefficients with document-specific simplex weights and parallelizing independent subproblems.
Identity Notes & Concept Scope
This is the fitting procedure named in Section 3 of Inouye et al. 2014, distinct from the APM probability-model construction, generic pseudolikelihood estimation and posterior EM. Its defining split yields word-specific coefficient problems and document-specific simplex problems. The inspected released solver represents independent directed nodewise coefficients; model validity requires separate compatibility and normalization restrictions. It is not generic Newton optimization, QUIC itself or a particular trained topic model. No normalized identity match was found across all 442 pinned AIO labels and scoped synonyms and 421 preceding native IDs, names and aliases. Full-checkout fixed-string searches in worktree and main included ignored and hidden files. Ten matched lines in each checkout concern prior discovery references, raw search/abstract captures and downloaded-source metadata; these were classified by their file/field context and matched excerpts, not treated as ontology identities. All 192 semantic label/synonym hits were read. Nineteen exact annotated CLASS nodes and outgoing edges were inspected, with 13 verified equal to prior reading and six newly read. Thirty-four contextual YAMLs comprise 19 AIO and 15 native records; eight were fully read here, three final round99 records were hash-verified after full reading, and 23 were byte-verified after earlier full reading. Absence is bounded to the pinned snapshot, maintained corpus and inspected semantic neighborhood.
Claims & Grounded Evidence
2 Claims
Mechanism
#alternating-surrogate
For nonnegative count vectors x_i, K topics and simplex weights w_ij, define eta_is=sum_j w_ij*(a_js+sum_{t!=s} b_jts*x_it). Minimize F=(1/n)*sum_is[exp(eta_is)-x_is*eta_is]+lambda*sum_j,s,t!=s abs(b_jts), with unpenalized intercepts a_js and nonnegative lambda. Constants independent of fitted parameters are omitted. Fixing document weights gives separate convex penalized problems for each response word; fixing topic coefficients gives separate convex simplex problems for each document. Alternate the two blocks. The coefficient solver uses active/free coordinates, quadratic approximations, approximate coordinate-descent Newton directions and backtracking. The weight solver uses a quadratic approximation with pairwise coordinate transfers respecting the simplex. The paper traces decreasing regularization from an independent-component fit. These are point estimates under a surrogate, not posterior-responsibility E-steps, exact joint likelihood optimization or a globally convex joint problem.
Limitation
#implementation-boundary
The inspected v0.9.1 source uses raw counts and exponentiated linear predictors, fits asymmetric zero-diagonal nodewise coefficients, and returns those directed coefficient arrays. It does not impose the sufficient-statistic modifications, sign restrictions or joint-compatibility constraints needed to establish a proper positive-interaction Poisson MRF. The code normalizes initial document weights and retains unpenalized intercepts and 1/n component curvature scaling, clarifying omissions in the printed pseudocode. It also caps computed rates at 1e300; that numerical safeguard is not a normalized-model construction. Static inspection establishes these code paths, not the behavior of every historical experiment or unseen implementation.
⚠️ Curated Limitations & Negative Results
- Convexity of each fixed block does not imply joint convexity, uniqueness, global optimality or convergence for every approximate implementation. Degenerate curvature, numerical overflow and stopping tolerances require care; empirical parallel timing is not a universal complexity or speedup guarantee.
- Independent nodewise Poisson conditionals may be mutually incompatible. Even symmetrizing coefficients does not make unrestricted positive raw-count interactions normalizable. OR/AND edge support post-processing and coefficient averaging do not establish causal or conditional-independence semantics for an invalid joint model.
- For the stated average objective, the printed component gradient needs compatible matrix orientation, the augmented self-row index needs its intercept offset, and curvature terms require 1/n. The printed Armijo penalty difference lacks lambda. The released code resolves several of these notational issues but also omits lambda in that Armijo expression; a separate objective-decrease guard remains. No general convergence theorem is certified from the displayed pseudocode or this static code reading.
- In the release, the n>5000 block-gradient loop covers rows 1 through p although the augmented design has p+1 rows, omitting its final feature row. The simplex subsolver does not explicitly handle zero pair curvature. These bounded static observations are not a benchmark reproduction or a claim that every fitted result fails.
- The released core routines and options do not implement the papers beta pseudocount prior. The paper names additional experimental settings; their equivalence to this release is not assumed. Held-out selection fits document weights and compares the surrogate, not a verified exact marginal document likelihood.
- The model definition, raw regression surrogate and modified-statistic constructions must remain distinct. The separate APM-native model record requires a proper shared base distribution; this estimator does not automatically supply one.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:TrainingStrategy
TrainingStrategy
|
related_match | The local identity is a specified parameter-fitting algorithm. The pinned target uses a broad preprocessing/training description, so related match records its learning role without forcing an algorithm under that genus. |
AIO:ProbabilisticTopicModel
Probabilistic Topic Model
|
related_match | The algorithm was designed to fit a topic model. The AIO target is task-scoped; neither equivalence nor a model-family subclass assertion follows. |
Evidence Sources & Primary Literature
3 Sources| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
David I. Inouye, Pradeep Ravikumar, Inderjit S. Dhillon
|
primary paper
full_text
|
sha256:f38e28540906…
|
method-supplement
|
David I. Inouye, Pradeep Ravikumar, Inderjit S. Dhillon
|
primary paper
full_text
|
sha256:97c115b77a70…
|
author-code
|
David I. Inouye
|
official documentation
documentation
|
ID: https://github.com/davidinouye/apm/tree/1001dd0ab9ecfab6d02d79f2297df3daf6561301
sha256:62cc4a2a9741…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T23:32:13Z
Updated: 2026-10-11T23:32:13Z
Source File:
data/curated/ParallelAlternatingNewtonAPM.yaml